$\dfrac{ -10x - 8y }{ 2 } = \dfrac{ 5x + 5z }{ 3 }$ Solve for $x$.
Answer: Multiply both sides by the left denominator. $\dfrac{ -10x - 8y }{ {2} } = \dfrac{ 5x + 5z }{ 3 }$ ${2} \cdot \dfrac{ -10x - 8y }{ {2} } = {2} \cdot \dfrac{ 5x + 5z }{ 3 }$ $-10x - 8y = {2} \cdot \dfrac { 5x + 5z }{ 3 }$ Multiply both sides by the right denominator. $-10x - 8y = 2 \cdot \dfrac{ 5x + 5z }{ {3} }$ ${3} \cdot \left( -10x - 8y \right) = {3} \cdot 2 \cdot \dfrac{ 5x + 5z }{ {3} }$ ${3} \cdot \left( -10x - 8y \right) = 2 \cdot \left( 5x + 5z \right)$ Distribute both sides ${3} \cdot \left( -10x - 8y \right) = {2} \cdot \left( 5x + 5z \right)$ $-{30}x - {24}y = {10}x + {10}z$ Combine $x$ terms on the left. $-{30x} - 24y = {10x} + 10z$ $-{40x} - 24y = 10z$ Move the $y$ term to the right. $-40x - {24y} = 10z$ $-40x = 10z + {24y}$ Isolate $x$ by dividing both sides by its coefficient. $-{40}x = 10z + 24y$ $x = \dfrac{ 10z + 24y }{ -{40} }$ All of these terms are divisible by $2$ Divide by the common factor and swap signs so the denominator isn't negative. $x = \dfrac{ -{5}z - {12}y }{ {20} }$